This invaluable book is based on the notes of a graduate course on differential geometry which the author gave at the Nankai Institute of Mathematics. It consists of two parts: the first part contains an introduction to the geometric theory of characteristic classes due to Shiing-shen Chern and Andre Weil, as well as a proof of the Gauss-Bonnet-Chern theorem based on the Mathai-Quillen construction of Thom forms; the second part presents analytic proofs of the Poincare-Hopf index formula, as well as the Morse inequalities based on deformations introduced by Edward Witten.
- ISBN13 9789810246853
- Publish Date 25 September 2001
- Publish Status Active
- Publish Country SG
- Imprint World Scientific Publishing Co Pte Ltd
- Format Hardcover
- Pages 132
- Language English
- URL https://worldscientific.com/worldscibooks/10.1142/4756